The aim of this paper is to show, among other things, that, in separable Banach spaces, the presence of the smoothness with the highest derivative Lipschitzian implies the uniform Gâteaux smoothness of degree 1 up.
@article{urn:eudml:doc:38694, title = {Uniform G\^ateaux smoothness of higher order on separable Banach spaces.}, journal = {Extracta Mathematicae}, volume = {17}, year = {2002}, pages = {69-95}, zbl = {1006.46014}, mrnumber = {MR1914240}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38694} }
Bednarík, Dusan. Uniform Gâteaux smoothness of higher order on separable Banach spaces.. Extracta Mathematicae, Tome 17 (2002) pp. 69-95. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38694/